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Zeitschrift für Analysis und ihre Anwendungen


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Volume 40, Issue 1, 2021, pp. 33–50
DOI: 10.4171/ZAA/1671

Published online: 2021-01-25

Pseudo $S$-Asymptotically Bloch Type Periodicity with Applications to Some Evolution Equations

Yong-Kui Chang[1] and Yanyan Wei[2]

(1) Xidian University, Xi'an, China
(2) Xidian University, Xi'an, China

This paper is mainly focused upon the pseudo $S$-asymptotically Bloch type periodicity and its applications. Firstly, a new notion of pseudo $S$-asymptotically Bloch type periodic functions is introduced, and some fundamental properties on pseudo $S$-asymptotically Bloch type periodic functions are established. Then, the notion and properties of weighted pseudo $S$-asymptotically Bloch type periodic functions are similarly presented. Finally, the obtained results are applied to investigate the existence and uniqueness of pseudo $S$-asymptotically Bloch type periodic mild solutions for some semi-linear evolution equations in Banach spaces.

Keywords: Pseudo $S$-asymptotically Bloch type periodic functions, pseudo $S$-asymptotically $\omega$-anti-periodic functions, evolution equations

Chang Yong-Kui, Wei Yanyan: Pseudo $S$-Asymptotically Bloch Type Periodicity with Applications to Some Evolution Equations. Z. Anal. Anwend. 40 (2021), 33-50. doi: 10.4171/ZAA/1671